A new approach for recognizing handwritten mathematics using relational grammars and fuzzy sets

摘要

We present a new approach for parsing two-dimensional input using relational grammars and fuzzy sets. A fast, incremental parsing algorithm is developed, motivated by the two-dimensional structure of written mathematics. The approach reports all identifiable parses of the input. The parses are represented as a fuzzy set, in which the membership grade of a parse measures the similarity between it and the handwritten input. To identify and report parses efficiently, we adapt and apply existing techniques such as rectangular partitions and shared parse forests, and introduce new ideas such as relational classes and interchangeability. We also present a correction mechanism that allows users to navigate parse results and choose the correct interpretation in case of recognition errors or ambiguity. Such corrections are incorporated into subsequent incremental recognition results. Finally, we include two empirical evaluations of our recognizer. One uses a novel user-oriented correction count metric, while the other replicates the CROHME 2011 math recognition contest. Both evaluations demonstrate the effectiveness of our proposed approach.